Six times the cost price of a notebook is equal to five times the selling price of the notebook. If the selling price is Rs 10 more than the cost price find both the Cost Price and the Selling Price.

A total of Rs 20,000 is to be distributed among 100 persons as Prizes. A Prize is either Rs 100/- or Rs 500/-. Find the number of each type of prizes

Dear Student!

Here is the answer to your query.

**(1)** Let the cost price of the note book be Rs *x*.

Then the selling price of the note book will be Rs (*x* + 10).

**Given :** Six times cost price of notebook = Five times selling price of notebook

⇒ 6*x* = 5(*x* + 10)

⇒ 6*x* = 5*x* + 50

⇒ 6*x* – 5*x* = 50

⇒ *x* = 50

∴ Cost price of the notebook is Rs 50 and selling price of the notebook is Rs (50 + 10) = Rs.60

**(2)** Let the number of Rs 100 price be y

Then the number of Rs 500 price = 100 – y

**Given :** Rs 2000 is distributed as prizes

⇒ 100y + 500 ( 100 – y) = 20000

⇒ y + 5 ( 100 – y) = 200

⇒ y + 500 – 5y = 200

⇒ y – 5y = 200 – 500

⇒ – 4y = – 300

⇒ y = = 75

∴ The number of Rs 100 price is 75 and the number of Rs 500 prize is ( 100 – 75) = 25

Cheers!

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